Answered: Suppose f is differentiable on (0,1)…

Suppose f is differentiable on (0,1) and that there exists M > 0 so that |f′(x)|≤M for all x ∈(0,1). Prove that f is uniformly continuous on (0,1).

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter5: Rings, Integral Domains, And Fields

Section5.4: Ordered Integral Domains

Problem 8E: If x and y are elements of an ordered integral domain D, prove the following inequalities. a....

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Question

Suppose f is differentiable on (0,1) and that there exists M > 0 so that
|f′(x)|≤M for all x ∈(0,1).
Prove that f is uniformly continuous on (0,1).

With integration, one of the major concepts of calculus. Differentiation is the derivative or rate of change of a function with respect to the independent variable.

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